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3\left(ax^{2}-3ax-4a\right)
Factor out 3.
a\left(x^{2}-3x-4\right)
Consider ax^{2}-3ax-4a. Factor out a.
p+q=-3 pq=1\left(-4\right)=-4
Consider x^{2}-3x-4. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+px+qx-4. To find p and q, set up a system to be solved.
1,-4 2,-2
Since pq is negative, p and q have the opposite signs. Since p+q is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -4.
1-4=-3 2-2=0
Calculate the sum for each pair.
p=-4 q=1
The solution is the pair that gives sum -3.
\left(x^{2}-4x\right)+\left(x-4\right)
Rewrite x^{2}-3x-4 as \left(x^{2}-4x\right)+\left(x-4\right).
x\left(x-4\right)+x-4
Factor out x in x^{2}-4x.
\left(x-4\right)\left(x+1\right)
Factor out common term x-4 by using distributive property.
3a\left(x-4\right)\left(x+1\right)
Rewrite the complete factored expression.